Spin Foam State Sums and Chern-Simons Theory

Abstract

We review the spin foam state-sum invariants of 3-manifolds, and explain their relationship to manifold invariants coming from the Chern-Simons theory. We also explain the relationship between the known invariants of spin networks by using the Chain-Mail formalism of J. Roberts. This formalism can be understood as a quantum-group regularization of the BF theory path integrals.